Solve (5a^3b^-1)^-2

$$( 5 a ^ { 3 } b ^ { - 1 } ) ^ { - 2 }$$

Evaluate

$$\frac{b^{2}}{25a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{3}\times \frac{1}{b}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$5^{-2}\left(a^{3}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

Raise 5 to the power -2.

$$\frac{1}{25}\left(a^{3}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{25}a^{3\left(-2\right)}b^{-\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{25}\times \frac{1}{a^{6}}b^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{1}{25}\times \frac{1}{a^{6}}b^{2}$$

Expand

$$\frac{b^{2}}{25a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{3}\times \frac{1}{b}\right)^{-2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$5^{-2}\left(a^{3}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

Raise 5 to the power -2.

$$\frac{1}{25}\left(a^{3}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{25}a^{3\left(-2\right)}b^{-\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{25}\times \frac{1}{a^{6}}b^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{1}{25}\times \frac{1}{a^{6}}b^{2}$$